Goddyn, Luis; Richter, R. Bruce and Širáň, Jozef
(2007).
*Journal of Combinatorial Theory, Series B*, 97(6) pp. 964–970.

DOI (Digital Object Identifier) Link: | http://dx.doi.org/10.1016/j.jctb.2007.02.009 |
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## Abstract

We show that to each graceful labelling of a path on 2*s*+1 vertices, *s*≥2, there corresponds a current assignment on a 3-valent graph which generates at least 2^{2s} cyclic oriented triangular embeddings of a complete graph on 12*s*+7 vertices. We also show that in this correspondence, two distinct graceful labellings never give isomorphic oriented embeddings. Since the number of graceful labellings of paths on 2*s*+1 vertices grows asymptotically at least as fast as (5/3)^{2s}, this method gives at least 11^{s} distinct cyclic oriented triangular embedding of a complete graph of order 12*s*+7 for all sufficiently large *s*.

Item Type: | Journal Article |
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Copyright Holders: | 2007 Elsevier Inc. |

ISSN: | 0095-8956 |

Keywords: | graceful labelling; path; triangulation; complete graph; cyclic |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |

Item ID: | 23264 |

Depositing User: | Jozef Širáň |

Date Deposited: | 24 Sep 2010 15:09 |

Last Modified: | 15 Jan 2016 14:56 |

URI: | http://oro.open.ac.uk/id/eprint/23264 |

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